Configure custom git repository
At this moment, each API management instance offers a git repository which can be used to make changes to the instance. In DevOps scenarios where one team has multiple instances (dev, staging, prod) you want these changes to follow the product lifecyle along with other changes. For example: a certain release includes a new back-end API which you also want to include into APIM. You'd want the entire package to move from development into staging in one single release.
Imho the perfect way to fix this is to hook-up each APIM release to a centralized github repo, and have it sync up with new changes in a specific branch. This would also be more in-line with how app services for instance work. Having the built-in repo for single-instance scenarios is fine, but for multi-instance scenarios a centralized repo would fit much better.
Please see http://aka.ms/apimdevops for (work in progress) guidance and tools around automating deployment across multiple API Management environments.
Robert Abraham commented
We want this for a different reason. Our company has an organization in Github, and all of our source-controlled assets are in private repos that belong to that organization. Having a separate git repo just for APIM adds complexity to our workflow that we'd like to avoid. It would be ideal to be able to tie an APIM instance to a dedicated private Github repo that belongs to our organization.